Problem: Multiply. $0.6 \times 0.36=$
Solution: $6 \times 36$ and $0.6 \times 0.36$ multiply the same digits in the same order. So, the product of both problems will also have the same digits in the same order. Let's multiply $6 \times 36$. Then we can estimate to place the decimal point in the product of $0.6 \times 0.36$. $\begin{aligned} 36&\\ \underline{ \times 6}&\\ 36}\\ \underline{+180}}\\ 216 \end{aligned}$ Let's estimate to place the decimal in $0.6\times 0.36$. $\begin{aligned} 0.6 \times 0.36 &\approx 0.6\times 0.4\\\\ \phantom{0.6 \times 0.36} &\approx \dfrac6{10}\times \dfrac4{10}\\\\ \phantom{0.6 \times 0.36} &\approx \dfrac{24}{100}\\\\ &\approx 0.24 \end{aligned}$ Where can we place the decimal in $216$ to get a product close to $0.24$ ? $0.6 \times 0.36 = 0.216$